• The level at which a certain toxin causes the fish caught in fresh water lakes to be toxic is an average of 240 parts per million (it takes one year for the fish to be safe to eat again.) Consider the case of a local environmental group and a paper mill (employing 100 people, and taking 2 months to restart if it is stopped for retooling) that outputs some of that toxin into the local lakes. Tests of the pollutant level in the lake are conducted on a randomly chosen day each month.
  a) What null and alternate hypothesis would the environmental group prefer to be used in determining whether the plant should be retooled? What would the effects of a type I and type II error be? What would the effects of a large and a small alpha levels be?
  b) What null and alternate hypothesis would the paper mill presumably prefer to be used in determining whether the plant should be retooled? What would the effects of a type I and type II error be? What would the effects of a large and a small alpha levels be?
• Give three advantages and one disadvantage of using p-values in hypothesis testing instead of critical regions.
• Pg. 384: 9.38b Be sure to state the null and alternate hypothesis (defining any parameters you use), and state your conclusion.
• Pg. 401: 9.83 Show all work for credit.
• Some computer programs only return p-values for testing the alternate hypothesis "not equal". Say the program SAS returns a t-value of 1.3 and a p-value of 0.334 for testing the null hypothesis mu=10 vs. the alternate of mu is not equal 10. What would the p-value be for testing the alternate mu < 10? mu > 10? (Hint: Draw the picture!)

• Pg. 224: 5.60 a) Solve this problem using the appropriate probability function; b) Find an approximate solution by using the normal approximation and the continuity correction factor; c) Why should you know in advance that your use of the central limit theorem in part b shouldn't be accurate to very many decimal places?
• Pg. 383: 9.32 Use a computer or calculator for a, but do part b by hand. Also, what type of plot would you use to check that the normality assumption was true?
• Pg. 397: 9.64 Also, check that n is large enough to trust the confidence interval.
• Pg. 399: 9.71a (No work, no credit)

• Pg. 244-245: 6.20b,c; 6.22b, 6.24b
• Pg. 255: 6.48
• Pg. 269: 6.76
• Pg. 292: 7.24a-d (note a&d should say "approximately")

• Pg. 214: 5.34, also
  c) What does Chebyshev's theorem say about the answer to question b?
  d) Explain briefly why this is a probability distribution
  e) Construct a histogram for this probability distribution.
• For a group of 50 students, in how many ways can a 1st, 2nd, and 3rd place, and four honorable mentions be selected?
• Pg. 223: 5.48, also
  b) Use the formula to find P(exactly 2 fives are observed)
  c) Find P(2 or fewer fives are observed) {you may do this by hand, or by using a calculator or computer... say which you used}
  d) Find the mean and standard deviation of X=#fives observed

2) Consider the problem of determining the number of parking places for a 300-unit apartment complex near campus. You are given that "the typical number of cars per apartment is 1.2".
a) Why can you be sure that 1.2 must be the mean, and can't be the median, mode, or midrange?
b) How many parking spaces would be required to accomodate 95% of all the cars in the complex?

3) For the set of lengths 2 cm, 4 cm, 7 cm, 8 cm, and 9 cm, calculate the mean, median, mode, midrange, range, variance and standard deviation by hand.

4) Consider the data set and statistics in problem 3. If you were to add the same number (not 0!) to all of the observations in the data set how would the 7 statistics calculated change?

5) Consider the data set and statistics in problem 3. If you were to multiply all of the observations by the same number (not 0 or 1!) how would the 7 statistics calculated change.